Entanglement Spectrum of Composite Fermion States in Real Space

TL;DR

This paper analyzes the entanglement spectra of composite fermion states in fractional quantum Hall systems, introducing Entanglement Wave Functions that exactly describe low angular momentum sectors and explain excitation branches.

Contribution

It introduces Entanglement Wave Functions that fully characterize the entanglement spectra of composite fermion states in real and particle space.

Findings

Entanglement Wave Functions describe the entanglement spectra.

Exact low angular momentum sector descriptions for Laughlin and Jain states.

Physical explanation of excitation branches in the entanglement spectrum.

Abstract

We study the entanglement spectra of many particle systems in states which are closely related to products of Slater determinants or products of permanents, or combinations of the two. Such states notably include the Laughlin and Jain composite fermion states which describe most of the observed conductance plateaus of the fractional quantum Hall effect. We identify a set of 'Entanglement Wave Functions' (EWF), for subsets of the particles, which completely describe the entanglement spectra of such product wave functions, both in real space and in particle space. A subset of the EWF for the Laughlin and Jain states can be recognized as Composite Fermion states. These states provide an exact description of the low angular momentum sectors of the real space entanglement spectrum (RSES) of these trial wave functions and a physical explanation of the branches of excitations observed in the RSES of the Jain states.